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CEE 5324 –Advanced Hydrology – Lecture 14
Flood Frequency: Concepts and Tools
Glenn E. Moglen
Department of Civil & Environmental
Engineering
Virginia Tech
Today’s Agenda
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Please turn off all cell phones!
Questions?
Suggested Reading: Chow Chapter 12
Flood Frequency
 Frequency Analysis
 Calculating/Graphing Population Curve
 Normal and Log-normal distributions
 Tools: Matlab & Excel
 Obtaining and Manipulating Flood Data
 The need for “LPIII”
Probability Tables: “z”
Probability Tables: Other ways…
 In Excel, to get z=f(probability) use:
 Cell Formula: =NORMINV(0.95, 0, 1)
Probability
Mean Std. Dev.
 Above cell formula returns: z=1.644….
 In Excel, to get probability=f(z) use:
 Cell Formula:
Cum. Dist.
=NORMDIST(1.644954, 0, 1, TRUE)
z
Mean
Std. Dev.
 Above cell formula returns: p=0.95…
Flood Frequency Tools:
 Matlab programs
 gen_probplot.m
 probplot.m
 Excel spreadsheet:
log_probability_plot.xls
 PeakFQ (coming next time)
Flood Frequency Tools: Matlab
 gen_probplot.m
 Place text datafile (assumed
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“moglandia.txt”) and gen_probplot.m file
in same directory (assumed “c:\cee5324”)
Change to correct directory:
>> cd c:\cee5324
Load vector (column) of data into matlab:
>> load ‘moglandia.txt’
Store loaded data in “a” variable:
>> a = moglandia;
Set “lognorm” variable (1=log-normal,
0=otherwise)
>> lognorm = 0 (or lognorm = 1)
Flood Frequency Tools: Matlab
 probplot.m
 Place “moglandia.txt” probplot.m file in
same directory (assumed “c:\cee5324”)
 Change to correct directory:
>> cd c:\cee5324
 Program automatically loads
“moglandia.txt”, edit program if other text
filename
 Program automatically assumes log-normal
probability distribution and labels y-axis as
being discharge.
Flood Frequency Tools: Excel
 log_probability_plot.xls
 Paste downloaded data from USGS website
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in columns A (flood date) and B (peak flow).
Place sorted (largest to smallest) flows in
column D
Adjust formula in column F so it uses
correct “n” value for plotting position
formula
Adjust formulas in G3, G4, G5 for correct
number of years of observed data
Adjust vertical axis on “Chart” tab for
appropriate range of flood data.
Obtaining Flow Data:
 Daily Flows:
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http://waterdata.usgs.gov/nwis/dv
 Annual Maxima:
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http://nwis.waterdata.usgs.gov/usa/nwis/peak
Use only this USGS site for
flood frequency analysis
Obtaining, Plotting, and Analyzing
actual data
 From USGS Peak flow site
 Use query builder to select gage location
 “Output formats”: Choose “Tab-separated”
or “peakfq” format
 Download resulting data, import into Matlab
or Excel for further manipulation and
analysis
Plotting actual data
i
p
n 1
 Plotting position equation (Weibull):
6
Annual Peak Discharge, (ft 3/s)
10
5
10
4
10
99
95
90
80 70 60 50 40 30 20
10
5
Annual Exceedence Probability, (%)
1
Plotting Population Curve: Log-normal
 For New River at Radford we get:
 Mean of log(Q)’s:
X  4.61
 Standard Deviation of log(Q)’s:
S  0.241
 Population Curve:
log( Q)  X  S  z  4.61  (0.241)  z
 If p=0.5, z =0.0
log( Q)  4.61  (0.241)  (0.0)  4.61
Q  40,700 ft 3 /s
Plotting population curve: Log-normal
6
Annual Peak Discharge, (ft3/s)
10
5
10
4
10
99
95
90
80 70 60 50 40 30 20
10
5
Annual Exceedence Probability, (%)
1
Comparison of Frequency
Distributions
Log-normal distribution
Log-Pearson Type III distribution
Calculating sample statistics
 To plot population curve, first need these
moments:
 Mean:
1 n
X  Xj
n j 1
 Standard Deviation:
 1
2
X j  X  
s

 n  1 j 1

n
 Skew (needed if doing LPIII):
n X j  X 
n
G
3
j 1
(n  1)( n  2) s 3
0.5
Plotting Population Curve-LPIII
 For New River at Radford we get:
 Mean of log(Q)’s:
X  4.61
 Standard Deviation of log(Q)’s:
S  0.241
 Skew:
G  0.707
 Population Curve:
log( Q)  X  SK  4.61  (0.241)  K
 If p=0.5, K=-0.11578
log( Q)  4.61  (0.241)  (0.11578)  4.58
Q  38,200 ft 3 /s
Plotting population curve-LPIII
6
Annual Peak Discharge, (ft3/s)
10
5
10
4
10
99
95
90
80 70 60 50 40 30 20
10
5
Annual Exceedence Probability, (%)
1
Plotting population curve - Comparison
6
Annual Peak Discharge, (ft3/s)
10
5
10
4
10
99
95
90
80 70 60 50 40 30 20
10
5
Annual Exceedence Probability, (%)
1
PEAKFQ
 PEAKFQ is a USGS program that automates the
Bulletin 17B flood frequency analysis procedure
in a relatively painless windows-driven interface.
http://water.usgs.gov/software/PeakFQ/code/5.2/DOS/PKFQWin_5.2.exe
Reasons to use PEAKFQ
 Reasons to use PEAKFQ
 Automates flood frequency analysis (FFA)
consistent with Bulletin 17B methods
 No more tedious hand calculations!
 Manages more elaborate analyses that:
 Automatically excludes data inappropriate
for FFA
 Automatically manages historic flood
information
 Performs FFA for various skew options
PEAKFQ: Skew Options
 Station Skew: the skew value derived using the
method of moments for the gage data as we
have previously learned.
 Generalized Skew: the skew value derived from
map at right:
 Weighted:
mixture of
Station and
Generalized
Skew.
PEAKFQ: Weighted Skew
 Example: New River at Radford, VA
 G = 0.707 (derived from observed flood record at station)
 G = 0.433 (derived from map on previous slide)
 MSEG = 0.303 (derived from map on previous slide)
 MSEG = 0.177 (see next slide)
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RESULT: GW = 0.606
PEAKFQ: MSE of Station Skew Coef.
 Example: New River at Radford, VA
 A=(-0.33) + 0.08 * 0.707 = -0.2734
 B=0.94 – 0.26 * 0.707 = 0.7562
 N=43 (see PEAKFQ output or simply count years in used
record between 1896 and 1938).
 MSEG = 10^([-0.2734] – 0.7562[log10(43/10)]) = 0.177
Reasons to use PEAKFQ
 Reasons to use PEAKFQ
 Automates flood frequency analysis (FFA)
consistent with Bulletin 17B methods
 No more tedious hand calculations!
 Manages more elaborate analyses that:
 Automatically excludes data inappropriate
for FFA
 Automatically manages historic flood
information
 Performs FFA for various skew options